computation and validation of the dynamic response …dtic.mil/dtic/tr/fulltext/u2/a591869.pdf ·...

Computation and Validation of the Dynamic Response Index (DRI) 6 August 2013 Dacie Manion

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4. TITLE AND SUBTITLE Computation and Validation of the Dynamic Response Index (DRI)

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6. AUTHOR(S) Dacie Manion

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Introduction • Motivation and background • DRI overview • 1-DOF and 3-DOF models • Usage • Validation • EARTH metric • Summary • Ongoing work

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DRI Code: Motivation • Develop a fast in-house code for calculating the

Dynamic Response Index (DRI) injury metric using test or simulation results as input.

• Code should be stand-alone in nature and should lend itself easily to process automation.


Test

Simulation

Acceleration data

DRI Code DRI

Injury Metric

Background • Various metrics are used to

predict the occupant response and evaluate the safety of vehicle designs in underbody blast events.

• Underbody blast events cause a predominant risk of thoraco-lumbar spine injury.

• The Dynamic Response Index (DRI) has been used historically as a metric for spinal compression.

4 UNCLASSIFIED: Distribution A. Approved for public release

From (NATO, 2007).

Dynamic Response Index (DRI)

• Measure of spinal injury risk that accounts for the time duration of a load.

• Occupant torso modeled as a spring-mass-damper system. • Calculated from maximum relative displacement between

the pelvis and upper torso.

• Tolerance level of 17.7 for 10% risk of AIS 2+ injuries.

ωn = natural frequency (of spring-mass system) δmax = maximum relative displacement g = gravitational acceleration


m

k c

1-DOF model Takes anthropomorphic test device (ATD) pelvis acceleration or seat acceleration as input (pelvis preferred).

Spine

Upper Torso

Pelvis

= k/m

=

x

x1

= (x1-x)


spinal compression δ = x1 – x

1-DOF Computational model Input time and acceleration •Time series •Triangular pulse

Simulation •Trapezoidal rule for

numerical integration • Spring and damper forces

DRI

Acceleration data from physical test:


Acceleration DRI

3-DOF model


• Takes hull acceleration as input. • Accounts for energy absorption by

the floor and seat. • Springs representing the floor and

seat are piecewise-linear. • The spring representing the spine is

still linear.

Sprin

g st

iffne

ss (k

)

Spring deformation (m)

Piecewise Linear Spring Stiffness

m3

m2

m1

k3 c3

k2 c2

k1 c1

x3

x2

x1

Seat/ Pelvis

Spine

Upper Torso

Floor

Hull

Seat EA

Floor EA

3-DOF Computational model Input time and acceleration •Time series •Triangular pulse

Simulation •Trapezoidal rule for

numerical integration • Spring and damper forces

DRI

Triangular pulse input data (from previously developed Excel code):


Acceleration DRI

• Written in Python. • Requires Python

2.7+ and matplotlib plotting library.

• Executed from command line.

• Allows several optional arguments.

• Runs on Windows, Linux, UNIX, and Mac OS X.


DRI Code Outputs from 1-DOF code with triangular

pulse input

User manual

• Explains input formatting and output files generated.

• Includes example command-line calls and full test cases.

• Test cases used to validate code against: – Previously developed Excel code – Known DRI values for several

physical tests


Validation

• Validated against Excel code for both 1-DOF and 3-DOF.

• Used physical test results with DRI calculations previously done in other software to further validate 1-DOF model.

• Validated 3-DOF model against 1-DOF model by setting very large spring constants.

12

DRI output from Excel: DRI output from Python:

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0 10 20 30 40 50 60

0.00

0 0.

005

0.01

0 0.

015

0.02

0 0.

025

0.03

0 0.

035

0.04

0 0.

045

0.05

0

DRI v

alue

Time (s)

Acceleration data from physical test:

Python output DRI vs. Time:

Triangular pulse input data with given time duration and peak acceleration:

Time (s)

EARTH Code: Motivation • Error Assessment of Response Time Histories (EARTH)

– Compares time histories to validate M&S results. – New rigorous, quantitative tool for in-house VV&A.

• MATLAB code delivered by the Automotive Research Center (ARC) with several papers but no user manual – (Pan, 2012) – (Sarin, 2008) – (Sarin et al., 2010)


Acceleration data

EARTH Code

Validation Metric

DRI v

alue

Time (s)

Time History 1

Time History 2

Time (s)

DRI V

alue

EARTH code • Combines existing measures and

algorithms. • Quantifies and separates error due to:

– Phase shift – Magnitude differences – Topology (shape) discrepancy

• Takes two time histories as inputs along with a few parameters.

• Outputs: – Plots of original, shifted, and warped

time histories – Derivatives of shifted and warped

time histories – Error metrics for phase, magnitude,

and topology – Uses Bayesian framework to

determine model confidence for original, phase-shifted, warped, and warped derivative data.


Time

Acce

lera

tion

EARTH code validation


• ARC provided electrothermal battery model example: • Test vs. simulation data for

terminal voltage. • EARTH input parameters.

• Used to ensure code was working properly.

• Results were consistent with those of the ARC (Pan, 2012).

Error Metric Result

Phase 1

Magnitude 0.0017

Topological 0.4511

Time

Time

Term

inal

vol

tage

(V)

Term

inal

vol

tage

(V)

Simple test of EARTH code • Compared Excel output vs. Python

output for 1-DOF DRI model. Used triangular pulse input data with: • Input peak acceleration • Input time duration

• Down-sampled from ~25,000 to ~1200 data points to reduce computation time.

• Very low error across each category as expected.


Error Metric Result

Phase 1

Magnitude 0.0011

Topological 0.0058

Time (s)

Time (s)

Acce

lera

tion

(m/s

^2)

Acce

lera

tion

(m/s

^2)

Phase shift test of EARTH code • Introduced a phase shift of

1000 data points in the original vector.

• Down-sampled to ~800 data points. (phase shift of 33)

• EARTH code recognized and handled the phase shift, yielding low magnitude and topological error again as expected.


Error Metric Result

Phase 34

Magnitude 0.0022

Topological 0.0103

Time (s)

Time (s)

Acce

lera

tion

(m/s

^2)

Acce

lera

tion

(m/s

^2)

Validation of EECS models Case 1 Case 2


Error Metric Result

Case 1

Phase 3

Magnitude 0.4508

Topological 0.7635

Case 2

Phase 4

Magnitude 0.6779

Topological 0.8296

Time

Time

Time

Time

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Acce

lera

tion

(g)

Original data from drop tower tests.

Ongoing work • Write EARTH code user

manual for in-house use at TARDEC.

• Use DRI code to help evaluate new concept vehicles for DARPA.

• Update Hybrid Lumped-Finite Element (HLF) code (HyperMesh script for generating hull models) to add 3-DOF occupant models.


V-hull model from HLF code

Summary 1. DRI

– Developed 1-DOF and 3-DOF code in Python. – Validated against Excel code and physical test results. – Documented usage and examples.

2. EARTH code – Learned and tested EARTH code. – Gathered example I/O data. – Applied to EECS Team data to support in-house

model VV&A efforts. – Documented code for future VV&A at TARDEC.

3. Summarized all work in a technical report.


References • NATO Science and Technology Organization. Test

Methodology for Protection of Vehicle Occupants against Anti-Vehicular Landmine Effects. RTO-TR-HFM-090 AC/323(HFM-090)TP/72, Technical Report, April 2007.

• Pan, H. (2012), On the Integration of EARTH metric into the Bayesian Validation Framework, Technical Report, University of Michigan, Ann Arbor, MI, USA.

• Yorra, A.J. (1956), The Investigation of the Structural Behavior of the Intervertebral Discs, Masters Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA.

• Ruff, S. (1950), Brief Acceleration: Less than One Second, German Aviation Medicine in World War II, Vol. I, Chapter VI-C, Department of the Air Force.

• Ramalingam, J. and R. Thyagarajan. (2013, Jan 23). Design and Analysis of Vertically Stroking Floors (OCP-TECD). Technical briefing.

• Sarin, H. (2008), Error Assessment of Response Time Histories (EARTH): A metric to validate simulation models, M.S. Thesis, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA.

• Sarin, H., Kokkolaras, M., Hulbert, G., Papalambros, P., Barbat, S., and R.-J. Yang (2010), Comparing Time Histories for Validation of Simulation Models: Error Measures and Metrics, Journal of Dynamic Systems, Measurement, and Control, Vol. 132, pp. 061401-1 – 061401-10.


• Matt Castanier • Ravi Thyagarajan • Sara Pace • Hao Pan • Gregory Hulbert • Michael Kokkolaras

Acknowledgments

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